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Simplifying 5n + 17.5 + -4n = 13(n + -2) + -19.7 Reorder the terms: 17.5 + 5n + -4n = 13(n + -2) + -19.7 Combine like terms: 5n + -4n = 1n 17.5 + 1n = 13(n + -2) + -19.7 Reorder the terms: 17.5 + 1n = 13(-2 + n) + -19.7 17.5 + 1n = (-2 * 13 + n * 13) + -19.7 17.5 + 1n = (-26 + 13n) + -19.7 Reorder the terms: 17.5 + 1n = -26 + -19.7 + 13n Combine like terms: -26 + -19.7 = -45.7 17.5 + 1n = -45.7 + 13n Solving 17.5 + 1n = -45.7 + 13n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13n' to each side of the equation. 17.5 + 1n + -13n = -45.7 + 13n + -13n Combine like terms: 1n + -13n = -12n 17.5 + -12n = -45.7 + 13n + -13n Combine like terms: 13n + -13n = 0 17.5 + -12n = -45.7 + 0 17.5 + -12n = -45.7 Add '-17.5' to each side of the equation. 17.5 + -17.5 + -12n = -45.7 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -12n = -45.7 + -17.5 -12n = -45.7 + -17.5 Combine like terms: -45.7 + -17.5 = -63.2 -12n = -63.2 Divide each side by '-12'. n = 5.266666667 Simplifying n = 5.266666667
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